The Definition of Points
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From: Mike Kelly on 31 Mar 2007 19:51 On 31 Mar, 16:47, Tony Orlow <t...(a)lightlink.com> wrote: > Mike Kelly wrote: > > On 31 Mar, 13:48, Tony Orlow <t...(a)lightlink.com> wrote: > >> step...(a)nomail.com wrote: > >>> In sci.math Virgil <vir...(a)comcast.net> wrote: > >>>> In article <460d4...(a)news2.lightlink.com>, > >>>> Tony Orlow <t...(a)lightlink.com> wrote: > >>>>> An actually infinite sequence is one where there exist two elements, one > >>>>> of which is an infinite number of elements beyond the other. > >>>> Not in any standard mathematics. > >>> It is not even true in Tony's mathematics, at least it was not true > >>> the last time he brought it up. According to this > >>> definition {1, 2, 3, ... } is not actually infinite, but > >>> {1, 2, 3, ..., w} is actually infinite. However, the last time this > >>> was pointed out, Tony claimed that {1, 2, 3, ..., w} was not > >>> actually infinite. > >>> Stephen > >> No, adding one extra element to a countable set doesn't make it > >> uncountable. If all other elements in the sequence are a finite number > >> of steps from the start, and w occurs directly after those, then it is > >> one step beyond some step which is finite, and so is at a finite step. > > > So (countable) sequences have a last element? What's the last finite > > natural number? > > > -- > > mike. > > As I said to Brian, it's provably the size of the set of finite natural > numbers greater than or equal to 1. Provable how? > No, there is no last finite natural, You keep changing your position on this. > and no, there is no "size" for N. Aleph_0 is a phantom. When we say that a set has cardinality Aleph_0 we are saying it is bijectible with N. Are you saying it's impossible for a set to be bijectible with N? Or are you saying N does not exist as a set? Something else? I find it very hard to understand what you are even trying to say when you say "Aleph_0 is a phantom". It seems a bit like Ross' meaningless mantras he likes to sprinkle his posts with. -- mike.
From: Lester Zick on 31 Mar 2007 19:53 On Fri, 30 Mar 2007 12:04:33 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>>>>> Okay, Tony. You've made it clear you don't care what anyone thinks as >>>>>> long as it suits your druthers and philosophical perspective on math. >>>>>> >>>>> Which is so completely different from you, of course... >>>> Difference is that I demonstrate the truth of what I'm talking about >>>> in mechanically reduced exhaustive terms whereas what you talk about >>>> is just speculative. >>> You speculate that it's agreed that not is the universal truth. It's not. >> >> No I don't, Tony. It really is irritating that despite having read >> E201 and E401 you call what I've done in those root threads >> "speculation". What makes you think it's speculation? I mean if you >> didn't understand what I wrote or how it demonstrates what I say then >> I'd be happy to revisit the issue. However not questioning the >> demonstration and still insisting it's speculation and no different >> from what you say is just not okay. > >I've questioned that assumption all along. We've spoken about it plenty. What assumption, Tony?You talk as if there is some kind of assumption. >> I don't speculate "it's agreed" or not. I don't really care whether >> it's agreed or not and as a practical matter at this juncture I'd have >> to say it's much more likely not agreed than agreed. What matters is >> whether it's demonstrated and if not why not and not whether it's >> agreed or not since agreements and demonstrations of truth are not the >> same at all. Agreements require comprehension and comprehension >> requires study and time whereas demonstrations of truth only require >> logic whether or not there is comprehension. >> >> ~v~~ > >Demonstrate what the rules are for producing a valid one of your logical >statements from one or more other valid ones of your logical statements, >because "not not" and "not a not b" are not standard valid logic >statements with known rules of manipulation. What are the mechanics? As >far as I can tell, the first is not(not(true))=true and the second is >or(not(a),not(b)), or, not(and(a,b)). Or you could demonstrate why the standard valid logic you cite is standard and valid. ~v~~
From: Tony Orlow on 31 Mar 2007 19:53 Lester Zick wrote: > On Fri, 30 Mar 2007 12:24:12 -0500, Tony Orlow <tony(a)lightlink.com> > wrote: > >> Lester Zick wrote: >>> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >>> wrote: >>> >>>>>> Add 1 n >>>>>> times to 0 and you get n. If n is infinite, then n is infinite. >>>>> This is reasoning per say instead of per se. >>>>> >>>> Pro se, even. If the first natural is 1, then the nth is n, and if there >>>> are n of them, there's an nth, and it's a member of the set. Just ask >>>> Mueckenheim. >>> Pro se means for yourself and not for itself. >> In my own behalf, yes. >> >>> I don't have much to do >>> with Mueckenheim because he seems more interested in special pleading >>> than universal truth. At least his assumptions of truth don't seem >>> especially better or worse than any other assumptions of truth. >>> >>> ~v~~ >> He has some valid points about the condition of the patient, but of >> course he and I have different remedies. > > Some of which may prove deadly. > > ~v~~ Well, his mostly consist of amputation and leeches, but as long as he sticks to the extremities, I don't think death is inevitable... Mine don't actually break anything, except for the leeches, and some bones... 01oo
From: Lester Zick on 31 Mar 2007 19:55 On Fri, 30 Mar 2007 12:22:30 -0500, Tony Orlow <tony(a)lightlink.com> wrote: >Lester Zick wrote: >> On Thu, 29 Mar 2007 09:37:21 -0500, Tony Orlow <tony(a)lightlink.com> >> wrote: >> >>>> Finite addition never produces infinites in magnitude any more than >>>> bisection produces infinitesimals in magnitude. It's the process which >>>> is infinite or infinitesimal and not the magnitude of results. Results >>>> of infinite addition or infinite bisection are always finite. >>>> >>>>> Wrong. >>>> Sure I'm wrong, Tony. Because you say so? >>>> >>> Because the results you toe up to only hold in the finite case. >> >> So what's the non finite case? And don't tell me that the non finite >> case is infinite because that's redundant and just tells us you claim >> there is a non finite case, Tony, and not what it is. >> > >If you define the infinite as any number greater than any finite number, >and you derive an inductive result that, say, f(x)=g(x) for all x >greater than some finite k, well, any infinite x is greater than k, and >so the proof should hold in that infinite case. Where the proof is that >f(x)>g(x), there needs to be further stipulation that lim(x->oo: >f(x)-g(x))>0, otherwise the proof is only valid for the finite case. >That's my rules for infinite-case inductive proof. It's post-Cantorian, >the foundation for IFR and N=S^L. :) > >>> You can >>> start with 0, or anything in the "finite" arena, the countable >>> neighborhood around 0, and if you add some infinite value a finite >>> number of times, or a finite value some infinite number of times, you're >>> going to get an infinite product. If your set is one of cumulative sets >>> of increments, like the naturals, then any infinite set is going to >>> count its way up to infinite values. >> >> Sure. If you have infinites to begin with you'll have infinites to >> talk about without having to talk about how the infinites you >> have to talk about got to be that way in the first place. >> >> ~v~~ > >Well sure, that's science. Declare a unit, then measure with it and >figure out the rules or measurement, right? I have no idea what you think science is, Tony. Declare what and then measure what and figure out the rules of what, right, when you've got nothing better to do of an afternoon? ~v~~
From: Tony Orlow on 31 Mar 2007 19:55
Lester Zick wrote: > On 31 Mar 2007 10:02:17 -0700, "Brian Chandler" > <imaginatorium(a)despammed.com> wrote: > >> Tony Orlow wrote: >>> Brian Chandler wrote: >>>> Tony Orlow wrote: >>> Hi Imaginatorium - >> That's not my name - for some reason Google has consented to writing >> my name again. The Imaginatorium is my place of (self-)employment, > > And here I just assumed it was your place of self confinement. > >> so >> I am the Chief Imaginator, but you may call me Brian. > > Arguing imagination among mathematikers is like arguing virtue among > whores. > > ~v~~ So, what do you have against whores? 01oo |